Question

Dean entered his sister into their town's Smelly Shoe Competition. Dean observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes. What is the probability that a randomly selected contestant is not 31 to 50 years old and is not wearing tennis shoes?Simplify any fractions.

Tennis Shoes High Heels
Under age 12 4 2
13 to 30 years old 7 7
31 to 50 years old 6 6
17/32
15/16
13/32
9/32

Answer 1

First, let's find the total number of contestants who are not 31 to 50 years old and are not wearing tennis shoes:

- Under age 12: 2 (High Heels)
- 13 to 30 years old: 7 (Tennis Shoes) + 7 (High Heels) = 14
- 31 to 50 years old: We want to exclude this category, which contains 6 (Tennis Shoes) + 6 (High Heels) = 12 contestants

Therefore, the total number of contestants who are not 31 to 50 years old and are not wearing tennis shoes is 2 + 14 = 16.

Now, the total number of contestants is:
- Under age 12: 4 (Tennis Shoes) + 2 (High Heels) = 6
- 13 to 30 years old: 7 (Tennis Shoes) + 7 (High Heels) = 14
- 31 to 50 years old: 6 (Tennis Shoes) + 6 (High Heels) = 12

The total number of contestants is 6 + 14 + 12 = 32.

The probability that a randomly selected contestant is not 31 to 50 years old and is not wearing tennis shoes is 16/32 = 1/2.

So, the correct answer is 1/2, which can be simplified as 16/32 = 1/2.